TITLE: What are your favorite puzzles/toys for introducing new mathematical concepts to students?
QUESTION [31 upvotes]: We all know that the Rubik's Cube provides a nice concrete introduction to group theory.  I'm wondering what other similar gadgets are out there that you've found useful for introducing new math to undergraduates and/or advanced high school students.

REPLY [2 votes]: Prof. Pedro Roitmann of University of Brasilia built these wonderful 'multiplying bottles' for teaching some properties of equilateral hyperbolas: